An advanced Taylor’s Series Method to Obtain New Exact Travelling Waves Solutions of the Real-Valued Stochastic Ginzburg-Landau Equation

Abstract

The investigations on asymptotic, semi-analytic, and numerical methods, techniques, and algorithms cannot be overemphasized or exhaustive in the field of applied sciences; while several notable equations that arise in engineering and the applied sciences in general, from several works of literature, needs to be solved and simulated to enable accurate forecasting, also study the dynamical behaviour of the system or model. In this regard, a solitary wave solution has been obtained to the real-valued stochastic Ginzburg-Landau (G-L) equation forced in the Ito sense by a multiplicative parameter in this paper by merging a very recent Zainab-Mohammed-Alwan (ZMA)) integral transform with the projected differential transform. When this noise parameter takes an arbitrary and zero value, the results via tables and graphical illustrations demonstrate remarkable convergence to the exact solution as appeared in the pieces of literature. The dynamical behaviour investigation of the system via parameter effect plots also demonstrates an increase in the concavity and superposition for each increase in the noise parameter. Inevitably, this method has been confirmed to be a perfect asymptotic alternative for solitary wave solutions through hybrid algorithms on stochastic differential equations and wider classes of differential equations (partial and ordinary), as the results proffered by this proposed method appear to be rapidly convergent compared to analytical and exact solution achieved in published literature.